Gnome shell: pressing the super key does not work

Okay. You might have locked your super button.

Try unlock it on your keyboard. It usually has two icons - a window key and a lock.

In my case, I have unlocked the super button by pressing

Right Fn + F12

Then everything is working perfectly.

finally found it myself.

In older Ubuntu versions, go to System Settings > Keyboard Layout > Layouts and then choose Options.

In newer Ubuntu versions, install Tweaks (sudo apt install gnome-tweaks) and open it, then Keyboard & Mouse and then choose Additional Layout Options.

There is an option for the Alt/Win key behaviour and there I had the option selected Meta is mapped to Win keys.

Deselecting that option, and choosing Alt and meta are on Alt keys fixes it for me. At least the super is working again to access the Activities. Not quite sure what the impact is of this choice.

Under gnome 3.4.2.1, I had to use "Meta is mapped to Win keys". Now shortcuts with Super key work now.